Sketch-Up is not the right tool. I suggest a tool like Autodesk Inventor or SolidWorks. I don't know of any free 3D capable CAD that can do all the necessary statical and dynamical analysis. FreeCad is probably the closest.
Once you have a model built in 3D, including all the levers and mounts and bearings needed for servos/actuators and wiring, then run the numbers on weights and lengths to understand the needed torque of each link in the chain. Verify that the actuators you want to use can deliver, and then get the needed components and start prototyping. (Hint: Your actuators are unlikely to actually deliver what you need within whatever budget you have; the best cost trade-off is to accept much slower movement and thus get higher torque from gearing.)
If you already understand motion control, statics, and dynamics, this should just be a specific application of those skills. There's nothing "special" about arms as different from any other mechanical application from first principles.
Note that you should plan on spending at least twice as much money as the cost of the components you use in the final finished product; that ratio may go up even more depending on how close your initial plan is and how much you change your mind as you go along.
In the end, there is no substitute for actual, hands-on experience, and such experience will end up costing a lot in time and materials.